Richardson of the Hughes Research Laboratory for making facilities available that aided in the rapid completion of this work. Predictions will be given for the total decay rate and branching ratios of such a meson in terms of hypercharge coupling strength. Examples of both these aspects of high energy physics investigation will be found in the research summarized in this thesis.
In Chapter 4, we are primarily concerned with using this hypothesis to elucidate the role of the M-meson in the phenomena of strong interactions. Under the hypothesis that the K-n resonance is vectorial, we examine the role of K * in the concomitant production of A from n and in the production of A from K. A + K and K + N + A + 1 (, that the accompanying production amplitude in the forward direction (for K) at high energies is asymptotically equal to the negative of the characteristic amplitude.
We discuss the experiments needed to provide data for a test of the Regge pole hypothesis. If one of the observed three-pion I = 0 resonances can be described as a vector meson associated with a conserved hypercharge current, then one will be able to directly obtain a. These terms are the same as those associated with unstable particles, and the analysis of particle phenomena.
The expression for the degree of decomposition is complicated by the fact that the square of the matrix element is not constant and by necessity.
III.3)
III.6)
J (III.7)
DECAY OF THE X ~SON
Recent experimental evidence on the decay of the neutral meson at 550 Mev(6) into three pions suggests that for this object the most likely quantum numbers are (spin 0, parity -, G although statistical limitations and uncertainties in background subtraction do not command J1CG = 1- - must be excluded.lB). Since this neutral meson is known to have isospin I = 0,(19) if it were pseudo-scalar with G = +1, it would fit the description of the missing member, called X, of an. 2)". Consequently, it is very difficult to estimate their rates; perhaps the only statement one can trust is that the ratio of the.
A ratio(18) of neutral to charged decay modes of the 550 Mev meson near 3 implies that the two photon decay will be the dominant one. So we will essentially be able to give an estimate of the fraction of X's that fall into 1C+ + 1C- + y, a number that can be compared to experiment. The matrix element is considered to be that which results from the retention of only a jO meson intermediate state, which is.
The geometric factors in the last peak are identical to those in the rrx peak. X(mX -E+ -E-)/(mX -4m;); the integral over y can be done analytically, but the other must be done numerically. To complete the calculation, we need to be able to evaluate . ff'y)(/fyy)( ' We will do this by scattering the vertices, assuming a predominance of jO-meson and ro-meson intermediate states, and using the value for the ratio of ffX and 0Xl)'X vertices.
A resonance has been found in the K-~ system, which most likely has spin amount J 1. It is quite possible that this resonance belongs to the octet of vector mesons predicted by Gell-Mann and Ne'eman;. Two important general questions must be asked about this object: (1) How strongly it is bound to other particles. 2) Does the assumption that the M contribution dominates a given amplitude allow us to understand any important features of the reactions in which it is exchanged.
In Part II, the coupling strength of M with the K-~ system will be related to the resonance width. The same coupling constant is involved in the production of M in the reaction K + p~ M + p, which we will do. In Part III, the contribution of M to the associated production amplitude will be studied.
We will discuss the M there according to the Regge pole hypothesis, and discuss how experiments on beam take place. The crossed hyperon production reaction, KO + p -+ A + ~ +, will be explored in a similar vein in Part IV. MKn also plays a role in the pion pole approximation of the M production amplitude in the reaction K + N --f > M + N.
However, Ba~i-Beg and DeCelles(23) and Chan(24) have proposed fitting existing experimental data on the total production cross-section to the pawn pool approach. Theoretically, however, we have no reason to expect the pion pole to dominate the overall cross-section at such low energies, and one strongly suspects that any similarity would be coincidental. That this must indeed be the case has recently been demonstrated by a measurement of the total cross-section for MO production by the Alston group (25).
The amplitude contains only two independent functions of relativistic invariants and can be written as Only a system with unity hypercharge, zero baryonic charge and I = 1/2 can be exchanged in this channel. By developing the amplitude 1( + K ~ A + if in partial waves, as done in Appendix A, it can be shown that the exchange a.
III:5)
MKrr and Y~ are the coupling constants of the M to the Krr and theAN currents respectively, J.I.ANM is the anomalous magnetic moment in the. In these reduced expressions, E refers to the energy of the particle and q,r the magnitude of the three:-momentum in the center-of-mass system. This can be rewritten in terms of the functions A and B, in which case it becomes
It is essential that such experiments are performed for greater simplicity in the analysis of these reactions. To flip the baryon lines, we must also take into account the transformation of the Dirac matrices. We must emphasize that the line reversal result is a function of the clutch type.
This fact was noted by Bernstein and Weinberg in their discussion(37) of the possible existence of a scalar resonance in the K-n system. We suggest that the data on the spectrum and the rates be analyzed in terms of the following representations for the form factors: Use the tables of Brene, et a1. 42) we performed the calculation of the twelve numerical integrals that appear in the formulas for the decay rate.
The parameter C is proportional to the coupling constant of the M with the K-n current and to the constant in the weak coupling point of the M and the leptons. The s-wave segment of the Kn matrix element is proportional to the divergence, D(q2), of the matrix element. If the constant terms dominate the form factors, so does the ratio of the velocities to the spectra.
Determination of the pion spectrum in electron-donating decays provides a convenient way to measure the C/A ratio. 0- the decay of the f.-meson into four pions will be dominated by a two-step process. The magnitude of this coupling can be estimated from the width P and the decay estimate f v .
It is therefore important to be able to make estimates of the order of magnitude of the decay rates. Chew, Proceedings of the 1958 Annual International COhference on High Energy Physics at CERN, (CERN, Geneva, 1958) p.
